M2 842 181 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	10.4546	67.1642%	360000	287380170	1.7916	8.0049%	12.2462	69.7926%
Target	2⁶³	0.5615	65.0794%	16000	260000	0.0033	1.8280%	0.5648	65.7177%
Difference	+4	+9.8931	+2.0848%	+344000	+287120170	+1.7883	+6.1768%	+11.6814	+4.0749%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2842181	14936437154518820153	20	63.695	2627636514796 2² × 167 × 4481 × 877837	2011-02-01	4481	877837	0.8241	0.0058	0.0100
2842181	17786611591117384559801	23	73.913	3129042730057900 2² × 5² × 457 × 5387 × 12710081	2023-01-31	5387	12710081	678.85	0.0781	0.1448

exponent	prime factors	composite factor	digits	bits*
2842181	14936437154518820153 17786611591117384559801	265668606222560811661372686144629792469553	42	137.609

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.302%
2003-12-13	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.945%
2010-12-21	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.323%
2011-01-02	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.443%
2011-01-24	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.633%
2011-02-01	markr	tiny	125000	2781250			14936437154518820153	20	63.695	0.030	0.439	0.060	3.118%
2023-01-31	USAFSS	6917th_Scty_Sq	360000	287380170			17786611591117384559801	23	73.913	1.792	0.439	3.583	8.005%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-02-12	Sturle Sunde	giacco.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-

ECM factoring results:

Total ECM effort:	0.627 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.627

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-20	BigBrother	005	50000	5000000						3	0.313
2010-11-07	James Classen	towerofart	50000	5000000						3	0.313

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Chris Proctor		007F7177AA72F335	0.220
1999-09-22	curtisc	v4_computers	007F7177AA72F335	0.220

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22

Oliver Kruse

GTX-3

14936437154518820153

A097A4233DE45C__

2017-12-07

kkmrkkblmbrbk

c4.xlarge

14936437154518820153

A097A4233DE45C__

2023-02-01

LordJulius

WhiteBox

14936437154518820153

17786611591117384559801

A097A4233DE45C47

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 360000, B2 = 287380170 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 125000, B2 = 2781250 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront